Use the method of Variation of Parameters to find a particular solution to the 2nd order non-homogeneous linear differential equation [ y^{ prime prime}+4 y= sin ^{2}(2 x) ] given the general solution ( y_{c}=C_{1} cos (2 x)+C_{2} sin (2 x) ) to the associated homogeneous equation.

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Use the method of Variation of Parameters to find a particular solution to the 2nd order non-homogeneous linear differential equation  [ y^{ prime  prime}+4 y= sin ^{2}(2 x)  ] given the general solution  ( y_{c}=C_{1}  cos (2 x)+C_{2}  sin (2 x)  ) to the associated homogeneous equation.

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